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    i've been asked to sketch and then find the laplace transform of H ( t - 1 ) - H ( t -1).
    i have now idea where to start with the step function sketch, and couldn't make out what wiki was saying. could someone introduce the concept to me.
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    Is it a ceiling or floor function?

    Floor function means values are rounded down to the integer, ceiling is rounded up. (2.8 --> Floor = 2, it is too small for 3, Ceiling = 3 it is too big for 2)

    Either way, an example:

    Take the graph of y=x^2 ------- From each integer 'x = something' point, draw a line to the right (this is for a floor function) parallel to the x axis across until you are below the next number. Repeat.
    Eventually it will look like a set of stairs, with each step getting larger. That should be the graph

    (hope instructions were clear enough)
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    Well H(x) = \begin{cases} 1 & \text{if } x > 0 \\ 0 & \text{if } x < 0 \end{cases}. With yours (and I assume one of those - signs is meant to be a +), you need to consider what happens in the regions x<-1, -1<x<1 and x>1. In each region the function is constant, but it takes a different values. As such when you take the Laplace transform, your integral will actually need to be split into three bits.

    (Original post by Van Grall)
    Is it a ceiling or floor function?
    I imagine it's the Heaviside step function.
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    (Original post by nuodai)
    Well H(x) = \begin{cases} 1 & \text{if } x > 0 \\ -1 & \text{if } x < 0 \end{cases}. With yours (and I assume one of those - signs is meant to be a +), you need to consider what happens in the regions x<-1, -1<x<1 and x>1. In each region the function is constant, but it takes a different values. As such when you take the Laplace transform, your integral will actually need to be split into three bits.


    I imagine it's the Heaviside step function.
    they're all - (minuses)
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    (Original post by plmqaz)
    they're all - (minuses)
    But H(t-1)-H(t-1)=0, so it's unlikely that they're meant to all be minuses.
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    ****, last bracket is ( t - 2 ) sorry.

    so it'll be x<-2, -2<x<-1 and x>-1?
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    (Original post by nuodai)
    Well H(x) = \begin{cases} 1 & \text{if } x &gt; 0 \\ -1 & \text{if } x &lt; 0 \end{cases}.
    Surely not?
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    (Original post by nuodai)
    I imagine it's the Heaviside step function.
    haha. ok.

    I'm still learning from the very basic books my school has.

    On that note, could you recommend any for improvement? (and also is that the right question to ask?)
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    (Original post by plmqaz)
    ****, last bracket is ( t - 2 ) sorry
    Ah right; in that case the regions you need to consider are x&lt;1, 1&lt;x&lt;2 and x&gt;2.

    (Original post by Slumpy)
    Surely not?
    Sorry, I've got negative integers on the brain.

    (Original post by Van Grall)
    haha. ok.

    I'm still learning from the very basic books my school has.

    On that note, could you recommend any for improvement? (and also is that the right question to ask?)
    What level are you at? What are you interested in? Most of the books I'd recommend are undergraduate textbooks which are usually about specific fields of maths.

    As for more general stuff, a good book which has lots and lots of stuff in it is this one (most of it follows from A-level type stuff) but it's mostly geared towards applied maths, as you can tell from the title. It's over 1000 pages long, though, so not exactly something you'd sit down and read -- it's mostly for reference alongside stuff you're already doing. A nice short book which covers some of the very basic parts of pure maths is this one. And if you just want to read about maths for a bit of fun, then this is nice. And the final book I'll recommend is this -- it's not very relevant for most uni maths courses, but it's very relevant in modern mathematical research in topology, and is a pretty good read.
    [/thread-hijack]
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    (Original post by nuodai)
    Ah right; in that case the regions you need to consider are x&lt;1, 1&lt;x&lt;2 and x&gt;2.


    Sorry, I've got negative integers on the brain.
    are they meant to be positive?
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    (Original post by plmqaz)
    are they meant to be positive?
    Yes, when H(t) goes to H(t-1) the graph is shifted to the right.
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    (Original post by nuodai)
    What level are you at? What are you interested in? Most of the books I'd recommend are undergraduate textbooks which are usually about specific fields of maths.

    As for more general stuff, a good book which has lots and lots of stuff in it is this one (most of it follows from A-level type stuff) but it's mostly geared towards applied maths, as you can tell from the title. It's over 1000 pages long, though, so not exactly something you'd sit down and read -- it's mostly for reference alongside stuff you're already doing. A nice short book which covers some of the very basic parts of pure maths is this one. And if you just want to read about maths for a bit of fun, then this is nice. And the final book I'll recommend is this -- it's not very relevant for most uni maths courses, but it's very relevant in modern mathematical research in topology, and is a pretty good read.
    [/thread-hijack]
    Doing IB Higher, starting maths at uni in september.

    Thanks for the links, I doubt library would have them, but I'll search around or buy one.

    Interested in maths applied to economics (maybe econometrics), and, from what I know about number theory so far, number theory. I'm guessing number theory is covered on every uni maths course, but econometrics i'm not so sure.
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    (Original post by nuodai)
    ... when you take the Laplace transform, your integral will actually need to be split into three bits.
    In fact, you only need one integral here. (As two of them are obviously 0).
 
 
 
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